Does the mod square of the wave function always have to be real?

1. The problem statement, all variables and given/known data

Doing a bit of QM from Griffiths intro to QM and got stuck early on on the following worked example:



http://ift.tt/1q0Yk6L



I was under the impression that the mod square of the wave function ψ(x,t) should always be a positive, real number, but I cannot understand where the isin(2πt/h(E₂-E₁)) has gone in the last line. Perhaps I'm missing some simplification using trig identities perhaps?





2. Relevant equations







3. The attempt at a solution